# MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems

arXiv: https://arxiv.org/abs/2404.04735 · HTML: https://mlsanity.com/paper/2404.04735/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 23 references that are in the map.
- First posted on arXiv 6 Apr 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 18 of 18)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Capabilities of GPT-4 on Medical Challenge Problems](https://mlsanity.com/paper/2303.13375/) (2023)
- [A Prompt Pattern Catalog to Enhance Prompt Engineering with ChatGPT](https://mlsanity.com/paper/2302.11382/) (2023)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [The CoT Collection: Improving Zero-shot and Few-shot Learning of Language Models via Chain-of-Thought Fine-Tuning](https://mlsanity.com/paper/2305.14045/) (2023)
- [Boosting Logical Reasoning in Large Language Models through a New Framework: The Graph of Thought](https://mlsanity.com/paper/2308.08614/) (2023)

## Built on by (most cited first, 30 of 41)

- [From LLM Reasoning to Autonomous AI Agents: A Comprehensive Review](https://mlsanity.com/paper/2504.19678/) (2025)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [LLM Agents for Education: Advances and Applications](https://mlsanity.com/paper/2503.11733/) (2025)
- [A Survey of LLM-Driven AI Agent Communication: Protocols, Security Risks, and Defense Countermeasures](https://mlsanity.com/paper/2506.19676/) (2025)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [A Survey on LLM-based Multi-Agent System: Recent Advances and New Frontiers in Application](https://mlsanity.com/paper/2412.17481/) (2024)
- [KLASS: KL-Guided Fast Inference in Masked Diffusion Models](https://mlsanity.com/paper/2511.05664/) (2025)
- [X-MAS: Towards Building Multi-Agent Systems with Heterogeneous LLMs](https://mlsanity.com/paper/2505.16997/) (2025)
- [BlindGuard: Safeguarding LLM-based Multi-Agent Systems under Unknown Attacks](https://mlsanity.com/paper/2508.08127/) (2025)
- [Meta-Reasoner: Dynamic Guidance for Optimized Inference-time Reasoning in Large Language Models](https://mlsanity.com/paper/2502.19918/) (2025)
- [ReSo: A Reward-driven Self-organizing LLM-based Multi-Agent System for Reasoning Tasks](https://mlsanity.com/paper/2503.02390/) (2025)
- [Deliberate Reasoning in Language Models as Structure-Aware Planning with an Accurate World Model](https://mlsanity.com/paper/2410.03136/) (2024)
- [Heterogeneous Swarms: Jointly Optimizing Model Roles and Weights for Multi-LLM Systems](https://mlsanity.com/paper/2502.04510/) (2025)
- [MASLab: A Unified and Comprehensive Codebase for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2505.16988/) (2025)
- [Infant Agent: A Tool-Integrated, Logic-Driven Agent with Cost-Effective API Usage](https://mlsanity.com/paper/2411.01114/) (2024)
- [Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2508.08292/) (2025)
- [Synergizing Logical Reasoning, Knowledge Management and Collaboration in Multi-Agent LLM System](https://mlsanity.com/paper/2507.02170/) (2025)
- [CMCTS: A Constrained Monte Carlo Tree Search Framework for Mathematical Reasoning in Large Language Model](https://mlsanity.com/paper/2502.11169/) (2025)
- [ReasoningWeekly: A General Knowledge and Verbal Reasoning Challenge for Large Language Models](https://mlsanity.com/paper/2502.01584/) (2025)
- [To trust or not to trust: Attention-based Trust Management for LLM Multi-Agent Systems](https://mlsanity.com/paper/2506.02546/) (2025)
- [SV-LLM: An Agentic Approach for SoC Security Verification using Large Language Models](https://mlsanity.com/paper/2506.20415/) (2025)
- [From Proprietary to Open-Source: Bridging the Distribution Gap via Multi-Agent Protocol Distillation in Agentic Search](https://mlsanity.com/paper/2607.24280/) (2026)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Reducing Cognitive Overhead in Tool Use via Multi-Small-Agent Reinforcement Learning](https://mlsanity.com/paper/2508.08882/) (2025)
- [Teaching According to Students' Aptitude: Personalized Mathematics Tutoring via Persona-, Memory-, and Forgetting-Aware LLMs](https://mlsanity.com/paper/2511.15163/) (2025)
- [MAS-Shield: A Defense Framework for Secure and Efficient LLM MAS](https://mlsanity.com/paper/2511.22924/) (2025)
- [TopoDIM: One-shot Topology Generation of Diverse Interaction Modes for Multi-Agent Systems](https://mlsanity.com/paper/2601.10120/) (2026)
- [Breaking the Martingale Curse: Multi-Agent Debate via Asymmetric Cognitive Potential Energy](https://mlsanity.com/paper/2603.06801/) (2026)
- [Agent Q-Mix: Selecting the Right Action for LLM Multi-Agent Systems through Reinforcement Learning](https://mlsanity.com/paper/2604.00344/) (2026)
- [AgentGrad: Intervention-guided Prompt Optimization for Multi Agent Systems](https://mlsanity.com/paper/2609.08572/) (2026)

## Abstract (arXiv)

Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in advanced mathematical problems requiring complex, multi-step logical reasoning. To enhance their inferential capabilities, current research has delved into textitprompting engineering, exemplified by methodologies such as the Tree of Thought and Graph of Thought. Nonetheless, these existing approaches encounter two significant limitations. Firstly, their effectiveness in tackling complex mathematical problems is somewhat constrained. Secondly, the necessity to design distinct prompts for individual problems hampers their generalizability. In response to these limitations, this paper introduces the textitMulti-Agent System for conditional Mining (MACM) prompting method. It not only resolves intricate mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts. With the assistance of MACM, the accuracy of GPT-4 Turbo on the most challenging level five mathematical problems in the MATH dataset increase from 54.68%  to  76.73%. The code is available in urlhttps://github.com/bin123apple/MACM.